Must Be True Classification
Must Be True Classification problems present a set of premises followed by statements that need to be classified as 'Must be true', 'Could be true', or 'Must be false' based on the given information. These problems test your ability to distinguish between necessary, possible, and impossible conclusions.
What You'll Learn
Introduction to Must Be True Classification
Must Be True Classification problems present a set of premises followed by statements that need to be classified as 'Must be true', 'Could be true', or 'Must be false' based on the given information. These problems test your ability to distinguish between necessary, possible, and impossible conclusions.
Prerequisites
How to Solve Must Be True Classification Problems
Step 1: Analyze the premises and understand what they establish
Step 2: For each statement to classify, ask three questions
Step 3: 'Must be true' - Is the statement true in every possible scenario consistent with the premises?
Step 4: 'Could be true' - Is there at least one scenario where the statement is true?
Step 5: 'Must be false' - Is the statement false in every possible scenario?
Step 6: Use Venn diagrams to test different possible configurations
Step 7: Classify each statement accordingly
Example Problem
Example: Premises: 'All students who passed the exam studied at least 10 hours. John studied 15 hours. Mary studied 5 hours. Sarah studied 10 hours exactly.' Classify: 'John passed the exam' Solution: Step 1: Premise: Passed → studied ≥ 10 hours (contrapositive: studied < 10 hours → did not pass) Step 2: John studied 15 hours (≥ 10) Step 3: Does this guarantee John passed? No - the premise says if passed then studied ≥10, not that studying ≥10 guarantees passing Step 4: John could have passed or failed (both are possible) Step 5: Therefore, 'John passed' is possible but not necessary Answer: Could be true
Pro Tips & Tricks
- 'Must be true' = statement holds in all possible worlds consistent with premises
- 'Could be true' = statement holds in at least one consistent world
- 'Must be false' = statement holds in no consistent world (contradicts premises)
- The contrapositive of a true statement is also true
- The converse and inverse are not necessarily true
- Use Venn diagrams to test multiple possibilities
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Must Be True Classification. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Must Be True Classification is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Must Be True Classification?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: